$\overline{AB}$ = $\sqrt{74}$ $\overline{BC} = {?}$ $A$ $C$ $B$ $\sqrt{74}$ $?$ $ \sin( \angle BAC ) = \frac{7\sqrt{74} }{74}, \cos( \angle BAC ) = \frac{5\sqrt{74} }{74}, \tan( \angle BAC ) = \dfrac{7}{5}$
Solution: $\overline{AB}$ is the hypotenuse $\overline{BC}$ is opposite to $\angle BAC$ SOH CAH TOA We know the hypotenuse and need to solve for the opposite side so we can use the sine function (SOH) $ \sin( \angle BAC ) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{\overline{BC}}{\overline{AB}}= \frac{\overline{BC}}{\sqrt{74}} $ $ \overline{BC}=\sqrt{74} \cdot \sin( \angle BAC ) = \sqrt{74} \cdot \frac{7\sqrt{74} }{74} = 7$